Partial Probabilistic Addition: A Practical Approach for Aggregating Gas Resources
- Pierre Delfiner (Total S.A.) | Robert Barrier (Total)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- April 2008
- Document Type
- Journal Paper
- 379 - 385
- 2008. Society of Petroleum Engineers
- 5.6.3 Deterministic Methods, 2.4.3 Sand/Solids Control, 4.6 Natural Gas, 4.2 Pipelines, Flowlines and Risers, 5.8.7 Carbonate Reservoir, 4.6.2 Liquified Natural Gas (LNG), 3.3 Well & Reservoir Surveillance and Monitoring, 1.6 Drilling Operations, 7.5.1 Ethics
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The portfolio of gas sources to supply a liquefied-natural-gas (LNG) project may involve many diverse fields, each with its range of uncertainty and degree of maturity. For project approval, it is necessary to aggregate the reserves/resources of all these fields into project-level representative numbers, either deterministic or probabilistic.
Arithmetic addition of all low estimates (1P or P90) and all high estimates (3P or P10) is known to overstate the range of uncertainty. On the other hand, independent probabilistic addition tends to produce unrealistically narrow ranges. The correct answer would be obtained by using correlated addition, but this requires the estimation of all correlations between field-resource estimates.
This paper presents a simplified and pragmatic approach, partial probabilistic addition. A hierarchy of "resource containers?? is defined from individual reservoirs to total project level, and resources are aggregated from bottom upward using either arithmetic or probabilistic addition—whichever is more appropriate. This amounts to setting weak correlations to 0 and strong correlations to 1. Expert opinion is solicited only concerning the strength of dependencies, rather than being asked to specify elusive correlation coefficients.
The validity of the approach is investigated by applying partial probabilistic addition to a synthetic portfolio of fields with the same log-normal size distribution. The study indicates the feasibility of estimating a global P90 with a controlled error, whereas for a P10, the error can become quite large. The method is then discussed using a real LNG case study.
Partial probabilistic addition is a practical method. It is easy to understand and to explain. It can be summarized in a single table where a color code indicates how its value was calculated for each cell. These features facilitate technical interchange and quality control, which are key to reducing as much as possible the degree of arbitrariness inherent in the modeling of dependencies.
The portfolio of gas sources to supply gas to an LNG project may be very diverse. It may include associated gas from producing oil fields and nonassociated gas from fields at different stages of development. Some of these gas fields are producing, others are delineated but undeveloped, others are discovered but not delineated, and some are still explora¬tion targets. For nonoperated fields, there is little or no control on how resource figures are calculated. To support the final investment decision, the resources of all these fields need to be consolidated into project-level representative numbers. These may be deterministic estimates 1P/2P/3P of proved , proved + prob¬able, and proved + probable + possible volume, respectively, or probabilistic low, best, high estimates P90/P50/P10. For example, the three numbers 67/100/150 Bcf mean that there is a 90% chance of having 67 Bcf or more, a 50% chance of having 100 bcf or more, and a 10% chance of having 150 Bcf or more. The low value 1P or P90 is of special interest for project approval because it is compared with a predefined resources threshold. [According to SPE terminology the word "resources?? is used rather than "reserves?? when commerciality is not proved (SPE 2001).]
Producing an estimate of minimum resources that can be used reliably as a decision tool is no easy task. It involves two aspects: (a) Which numbers to add? and (b) how to add them? The first question refers to the longtime debate between deterministic and probabilistic estimates. Deterministic 1Ps used for booking reserves are by design very conservative. They certify a volume considered as proved today. However, this figure does not reflect the project 1P, the volume that can reasonably be expected in the future after planned fields have been brought on stream and delineation work has been completed. Such an estimate is better derived by probabilistic means.
Concerning the aggregation of estimates, in the deterministic approach there is little choice other than summing all 1Ps, all 2Ps, and all 3Ps. For probabilistic estimates, arithmetic summation of all low values (P90) and all high values (P10) is known to overstate the range of uncertainty. On the other hand, independent probabilistic addition tends to produce suspiciously narrow ranges. The correct procedure is a probabilistic addition taking into account the dependencies between field-resource estimates. Assessment of these dependencies is the key issue. Methodologies have been proposed to estimate correlations between fields in a semiqualitative manner through an analysis of commonalities between fields (Carter and Morales 1998; Van Elk et al. 2000). However, the practicality of these approaches is in question when dealing with a large number of fields and reservoirs. Interesting guidelines for the aggregation of estimates for public disclosure have also been drafted (SPE 2001; COGEH 2004), but the present paper does not address reporting issues.
A simplified and pragmatic approach, partial probabilistic addition , is proposed. Groups are formed containing fields that tend to be either dependent or independent, and their resources are summed accordingly by arithmetic or probabilistic addition. This amounts to setting weak correlations p to 0 and strong correlations to 1. The validity of this approach is first investigated using a synthetic example. Then the method is applied to determination of the global P90 of an LNG project.
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